The Biggest Problem with Your Pricing Model is Your Reserving Model - PowerPoint PPT Presentation

The Biggest Problem with Your Pricing Model is Your Reserving Model Southwest Actuarial Forum June 3rd Presenter: Chris Gross Gross Consulting

The Pricing Problem • Estimate discounted value of ultimate claim costs and expenses • Estimate differences across available rating characteristics Gross Consulting 2

The (incomplete) Solution • Build models based on the current diagonal only • Build models based on a common age of development Gross Consulting 3

(incomplete) Treatment of Loss Development • Develop all losses with a factors based on age • Reduce premium/exposure based on age • Include policy effective date as a variable • Only use the process to rank policies • Generally assumes all development is the same (wrong!) Gross Consulting 4

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The Mix Problem… An Example • Two classes of business – Class 1. • Faster developing • Lower ultimate loss ratio (60%) – Class 2 • Slower developing • Higher ultimate loss ratio (90%) • Class 2 has always been there, but only recently started growing significantly Gross Consulting 8

Different Development 100% 90% 80% Percent of Ultimate 70% 60% 50% Class 1 40% Class 2 30% 20% 10% 0% 1 2 3 4 5 6 7 8 9 10 Yr of Development Gross Consulting 9

The Triangle Loss as of: Year Premium Age 1 Age 2 Age 3 Age 4 Age 5 Age 6 Age 7 Age 8 Age 9 Age 10 2006 105 7.53 20.40 32.67 43.49 52.72 58.08 61.20 62.36 63.28 64.50 2007 105 8.06 20.72 32.65 43.52 54.68 60.16 63.87 64.15 63.71 2008 105 6.48 19.23 30.80 42.47 52.70 58.32 60.99 62.91 2009 105 7.21 19.21 30.81 42.44 52.93 59.64 61.78 2010 105 7.43 21.88 34.36 43.89 53.76 59.81 2011 105 6.76 19.19 33.07 43.90 54.42 2012 105 7.11 18.49 30.01 40.40 2013 120 8.44 22.18 37.25 2014 140 8.65 25.87 2015 160 9.81 Gross Consulting 10

Development Factors 2006 2.709 1.602 1.331 1.212 1.102 1.054 1.019 1.015 1.019 2007 2.571 1.576 1.333 1.256 1.100 1.062 1.005 0.993 2008 2.967 1.602 1.379 1.241 1.107 1.046 1.031 2009 2.666 1.604 1.378 1.247 1.127 1.036 2010 2.944 1.570 1.277 1.225 1.113 2011 2.840 1.724 1.327 1.239 2012 2.602 1.622 1.346 2013 2.630 1.679 2014 2.990 Last 3 2.740 1.675 1.317 1.237 1.115 1.048 1.018 1.004 1.019 Cumulative 9.108 3.324 1.984 1.506 1.218 1.092 1.042 1.023 1.019 Gross Consulting 11

True Loss Ratio vs Estimate 80.0% 75.0% 70.0% 65.0% 60.0% Estimate Actual 55.0% 50.0% 45.0% 40.0% Gross Consulting 12

Potential Differences • Industry classification • Geography • Deductible/Limit Profile • Size of account • Type of Claims • Etc. Gross Consulting 13

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Challenges to Building a Complete Model • An age old problem – Loss development occurs over time, mature periods are old – Immature claims contain information • Many facets of loss development • Helpful to concentrate on a single time ‐ step (e.g. beginning of quarter to end of quarter) Gross Consulting 19

Data Financial Data Exposure Characteristics Beginning Case Reserve Type Ending Case Reserve Product Payment in Period ZIP Code Timing Data Claim Characteristics Accident Quarter Loss Cause Report Quarter Loss Cause ‐ Detail Valuation Quarter Gross Consulting 20

Claim activity from the beginning of the quarter to the end of the quarter Does the What is the Claim Have a New Value? New Value? Did the Claim Close? Is there a Payment? How much is the Payment? Arrows indicate dependency on other results A number of available claim or exposure characteristics may have predictive value for any of these questions. Gross Consulting 21

Probability of a Claim Closing • Base probability of 71% • Modification of this probability by various claim characteristic values that were found to have predictive value Gross Consulting 22

Close Probability – Claim Age Gross Consulting 23

Close Probability – Loss Cause Gross Consulting 24

Close Probability – Accident Quarter Gross Consulting 25

Close Probability ‐ Product Gross Consulting 26

Probability of Change in Value (Given Not Closed) • Base probability of 37% • 4 characteristics found to be predictive Gross Consulting 27

New Claim Value (Given Changed but Not Closed) • Base factor of 1.98 to beginning case reserve • Modification to this linear relationship, as well as five additional predictive characteristics Gross Consulting 28

New Claim Value ‐ Case Reserve Gross Consulting 29

New Claim Value – Loss Cause Gross Consulting 30

New Claim Value – ZIP Code Number of ZIP Codes 100 10 20 30 40 50 60 70 80 90 0 0.6 ‐ 0.7 0.7 ‐ 0.8 0.8 ‐ 0.9 0.9 ‐ 1.0 31 1.0 ‐ 1.1 Factor 1.1 ‐ 1.2 1.2 ‐ 1.3 1.3 ‐ 1.4 1.4 ‐ 1.5 Gross Consulting 1.5 ‐ 1.6 1.6 ‐ 1.7

Bringing it together • Simulation can be used to project activity in the next quarter • It is necessary to project not only the predictive relationships, but also the residual error term. • Chain through quarters using information from the previous simulated quarter. • Store results, preferably at the claim level. Gross Consulting 32

Simulate Going Forward • Claim Development – Start with current inventory of open claims – For each open claim simulate a number of potential outcomes for the next time ‐ step (using the claims’ characteristics) – For those simulated claim ‐ paths that are still open simulate forward another time ‐ step. – Continue until all simulated claim ‐ paths are closed Gross Consulting 33

Claim 1 Gross Consulting 34

Claim 2 Gross Consulting 35

Claim 3 Gross Consulting 36

Grand Total Probability distribution of total payments 0 0.2 0.4 0.6 0.8 1 Gross Consulting 37

Grand Total Mean of total payments 0 0.2 0.4 0.6 0.8 1 Gross Consulting 38

Grand Total Current case reserves 0 0.2 0.4 0.6 0.8 1 Gross Consulting 39

Product 1 Product 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Product 3 Product 4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Gross Consulting 40

Loss Cause 1 Loss Cause 2 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Loss Cause 3 Loss Cause 4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Loss Cause 5 Loss Cause 6 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Gross Consulting 41

Emergence • After simulating claim development to ultimate, model emergence • Frequency • Severity • Report Lag Gross Consulting 42

Claim Emergence Ultimate Claim Severity Claim Development Simulation Report Lag Claim Frequency Arrows indicate dependency on other results A number of exposure characteristics may have predictive value for any of these questions. Gross Consulting 43

Emergence Simulation • Use written policies (w/ characteristics) simulate remaining emergence. • Generating loss date within this process allows accident period calculations • Also get losses associated with unearned premium • Inforce loss ratio distribution. Gross Consulting 44

Case Study ‐ Background • Capital Insurance Group • Reasons for interest in the approach – Validate ultimate selections made from traditional triangle ‐ based methods – Insights that can be gained by applying predictive modeling to reserving – Triangle segmentation ideas – Support pricing predictive modeling by using estimated ultimate claims as the target variable Gross Consulting 45

Case Study ‐ Background • Began the process in Q4 of 2015 • Analyzed Q4 2014 (1 Year Lag) to be able to compare against traditional approach • Involved three individuals in the actuarial department • Single line of business • Longer ‐ tailed LOB Gross Consulting 46

Learning Curve • Chris came for an initial in ‐ house training session • Met every couple of weeks to answer questions on software and get valuable feedback on progress Gross Consulting 47

Learning Curve • Main challenge was getting all the data into an acceptable format and gaining familiarity of the software functionality • Easy to use and really fast automated results after getting over the initial learning curve hump Gross Consulting 48

Case Study ‐ Process • Organized data • Built and refined the predictive models • Simulated development and emergence • Analyzed output vs. current reserve model vs. actual development Gross Consulting 49

Case Study – Selected Highlights Gross Consulting 50

Case Study– Selected Highlights Gross Consulting 51

Case Study– Selected Highlights Gross Consulting 52

Case Study – Overall Impressions • Challenges – Reconciliation with other analysis • Value – Depth of information available – Statistically significant segmentation – Visual aids for decision making are an invaluable part of the process – Easy to evaluate performance of one model iteration to the next Gross Consulting 53

Case Study – Thoughts for the future • Reserving • Pricing • Other Gross Consulting 54